Causal metric hypothesis

The causal metric hypothesis, which represents the purest form of causal theory, proposes that all metric properties, such as distance and time, arise from a single binary relation. For example, causal theory abstains from any independent notion of spacetime locality. Besides having the advantages of simplicity and economy, the causal metric hypothesis automatically resolves problems arising from the existence of distinct causal and metric structures, such as nonlocality of entangled states in quantum theory and time-travel paradoxes in general relativity.

The causal metric hypothesis, if correct, greatly simplifies and clarifies theoretical physics. In particular, it is the purest possible version of background independence. A theory is background independent if its entire structure is dynamical, rather than relying on a static embedding space in which the dynamical entities of the theory reside. In this sense, general relativity is background independent, while nonrelativistic quantum theory, quantum field theory, and string theory are background dependent. In fact, background dependent theories generally possess three distinct types of structures: background structures, dynamical structures, and causal structures. For example, string theory includes a background space, dynamical entities such as D-branes with metric structures, and the causal structure. Background independent theories such as general relativity eliminate the background structure, while possibly retaining some degree of distinction between metric and causal structures. The causal metric hypothesis goes further, by identifying metric properties as emergent entities arising from the causal structure.

The causal metric hypothesis does not attempt to settle philosophical issues involving causality itself. For instance, the phenomena of self-causation, uncaused events, first causes, terminal effects, infinite causal regression, and infinite causal progression, are all allowed by the causal metric hypothesis. The causal metric hypothesis merely states that a variety of a priori distinct phenomena are properties of a single binary relation. It says nothing about the actual properties of this relation. For example, closed timelike curves and “backward time travel” exist in universes for which the binary relation has cycles, while these phenomena are absent if the relation is acyclic. Either type of theory is consistent, and no paradoxes arise. Rather, one must simply decide which theory or theories best agree with observation.